Tank A initially contains 40 gallons of a salt solution. Pure water is poured into tank A...

Tank A initially contains 40 gallons of a salt solution. Pure water is poured into tank A at a rate of 2 gal/min. A drain is opened at the bottom of tank A so that salt solution flows directly from tank A into tank B at 2 gal/min, keeping the volume of the salt solution in tank A constant over time. Tank B initially contains 100 gallons of pure water. A drain is opened at the bottom of tank B so that the volume of solution in tank B remains constant over time. If x and y represent the salt content in tanks A and B, respectively, show that

Given that x(0) = 20, solve the first equation for x, substitute the result into the second equation, then show that

Write a function M-file to evaluate y at time t. Following the technique used in Examples 3–5, use your function to (i) construct a plot of the salt content in tank B over the time interval [0, 100], and (ii) use fminbnd to find the maximum salt content in tank B and the time at which this occurs.